# Precision in Calculations: The Importance of Using Averages Accurately

• Maria Meister
In summary, my coworker is arguing that we should use the entire number when calculating the average, while I am arguing that we should use the 7 or 8 digit answer to 3 sig figs. This leads to another problem, in that we are taking the result of multiplying a 4 digit sig fig number by our 3 digit sig fig average retention time. Does anyone agree with me that there are several problems with my co worker's thoughts on this? Any input would be wonderful. Additionally, any documents, reports, or just anything you can think of that gives details of using averages in calculations would be greatly appreciated. I have been looking on the internet for over 3 hours now trying to find something that says you should not use an average in a multiplication
Maria Meister
i am having a dispute with my co worker over a calculation. we are dividing two numbers to get an area retention time and recording to 3 sig figs. we must do this 5 times. then we take the average of the 5 numbers and record to 3 sig figs
i am arguing that we must use the entire number which is 7 or 8 digits long when we calculate the average. she is saying we can just add up the 5 area retention times and take the average of them. i do not agree with the because we are only recording the 7 or 8 digit answer to 3 sig figs as it is. to take the average of 5 numbers that are only recorded to 3 sig figs doesn't sound precise to me.
this leads to another problem. we are then taking the result which would be our average area retention time and using it in another calculation. the calculation involves multiplying a 4 digit sig fig number by our 3 digit sig fig average retention time.
does anyone agree with me that there are several problems with my co workers thoughts on this?
anyones input would be wonderful.
also any documents, reports, or just anything you can think of that gives details of using averages in calculations would be greatly appreciated.
i have been looking on the internet for over 3 hours now trying to find something that says you should not use an average in a multiplication calculation when you are trying to give an accurate result.
i would just love to stick it to this old cow who has caused me loads of problems

Rounding is done at the very very very end of any calculation.

Agreed whozum.

Especially when dealing with significant-figures and scientific-notations.

Rounding-off should be left to the end only, otherwise your bringing in the cumulative small amounts of error that the rounding of each part during the course of your calculation brings,
instead of only counting the one amount of error at the very end of your calculation, which will be much less error, and will provide a much more sound answer.

Cheers.

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